Find the solution of the system of equations. Answer with the solution, or with “all real numbers” if there are infinite solutions, or with “no solution” if there are no solutions.
7x + 2y = -33
-49x – 5y = 177
x =
y =
Solve the system of linear equations by substitution. Enter your answer as an ordered pair if the system has a solution. Otherwise, enter “all real numbers” if it has infinite solutions or “no solution” if it has no solutions.
y = 4x + 6
-4x + y = 6
Enter your answer
Let’s solve the first system of equations:
1. Equations:
[
7x + 2y = -33 quad text{(1)}
]
[
-49x – 5y = 177 quad text{(2)}
]
We can multiply equation (1) by 5 to eliminate (y):
[
35x + 10y = -165 quad text{(3)}
]
Next, we can multiply equation (2) by 2 to align the (y) coefficients:
[
-98x – 10y = 354 quad text{(4)}
]
Now, we can add equations (3) and (4):
[
(35x + 10y) + (-98x – 10y) = -165 + 354
]
This simplifies to:
[
-63x = 189
]
Dividing both sides by -63:
[
x = -3
]
Substituting (x = -3) back into equation (1):
[
7(-3) + 2y = -33
]
[
-21 + 2y = -33
]
[
2y = -12
]
[
y = -6
]
Thus, the solution is:
[
(x, y) = (-3, –